Question

If (vector) |A|=7 and (vector) |B|=11 and (vector) |A+B|=8, then what is |A-B| equal to?​

Answer 1

Answer:

If (vector) |A|=7 and (vector) |B|=11 and (vector) |A+B|=8, then what is |A-B| equal to?

Assuming that the vector that is being referred to is 2-dimensional:

Let A=ax+by , B=cx+dy

∴A+B=(a+c)x+(b+d)y

And A−B=(a−c)x+(b−d)y

Where the vectors x and y are orthogonal unit vectors

|A|=a2+b2−−−−−−√=7

|A|2=a2+b2=49

|B|=c2+d2−−−−−−√=11

|B|2=c2+d2=121

|A+B|=a2+c2+2ac+b2+d2+2bc−−−−−−−−−−−−−−−−−−−−−−−√

=48+2ac+121+2bd−−−−−−−−−−−−−−−−−√=170+2ac+2bd−−−−−−−−−−−−−√=8

∴2(ac+bd)=64−170=−106

So using this we can use a similar method for A−B :

|A−B|=a2+c2−2ac+b2+d2−2bd−−−−−−−−−−−−−−−−−−−−−−−√

=170−2(ac+bd)−−−−−−−−−−−−−√=170−(−106)−−−−−−−−−−−√=276−−−√=269−−√

or in decimal form ≈16.61

Explanation:

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